Subsurface Modifier on a cube versus just adding a sphere itself
Catmull-Subdividing a cube does not result in a sphere. You will need to cast to a sphere with &#8679; Shift&#9095; AltS To Sphere operation or a Cast modifier. This question covers that.

The sphere and the spherized cube may look similiar, but the topology is different.



The key advantages of the subdivided, spherized cube are


Even Topology The sphere has dense topology at the top and much less dense topology at its equator. If you want to sculpt or otherwise modify the spherical shape, you want to have similiarly sized faces everywhere.
A 90° rotated sphere would also not give the same results as a sphere with no rotation.
Only Quads In organic modeling, which uses subdivision, we strive for topology which main uses quads. The sphere has many triangles at it's poles. Triangles will produce unnatural creases in combination with the subdivision surface modifier.